Batch processes play an important role in high value added products, such as specialty polymers, pharmaceuticals or biotech materials. A batch process is a process which is inherently batch in nature. For example, the production of a specific pharmaceutical that starts in an initial state, moves through multiple states, and ends with the desired end product. The process may then be repeated with a new batch of starting materials. A batch process can also denote repeated operations procedures, such as delayed coking in oil refining technology, or repeated dynamic transitions like regular transitions from production grade A to production grade B.
Modeling and diagnostics of such manufacturing processes, variables of which follow trajectories (batches, operating procedures, transitions between process states/grades) are difficult to model due to their non-steady state nature. A method for aligning these trajectories for the whole duration is desired. Typically, the trajectories need to have equal length and the measurements should be aligned along the trajectory based on a unifying factor. This factor is sometimes called an indicator variable. A Euclidian distance between trajectories may alternatively be used.
Existing approaches along these lines result in constraints put on unifying factor values. Such approaches may also process or model a whole synchronized trajectory together as one object. Both of these approaches may result in limitations, such as requiring significant amounts of manual data pre-processing.